John Akinde's seventh goal for the Chairboys in the 56th minute handed Peter Taylor's men the points and heaped the pressure on the Bees, who fell to defeat at Dagenham.
Matt Phillips was shown a yellow card just five minutes in for Wycombe after he blasted the ball at goal after clearly being blown for offside.
But that was about as interesting as a terrible first half got, as both sides failed miserably to muster any attempts on goal.
A wild 25-yard effort from Phillips that hit the top of the Kenilworth Road stand and two horribly sliced strikes from Ian Henderson and Chris Martin for the hosts were all the crowd had to enjoy.
Mercifully the last minute of the half brought some goalmouth action as firstly Jon-Paul Pittman crossed from the left for Lewwis Spence to poke wide on the stretch.
Moments later Rossi Jarvis hit an angled ball into the box for Henderson to nod weakly towards Jamie Young from ten yards, only for the goalkeeper to easily gather.
After so long without a clear opening being created, a glorious chance presented itself to Wycombe just three minutes into the second period.
Gary Holt delivered an inch-perfect cross into the area for Akinde, but the Bristol City loanee wastefully planted his free header over the bar from six yards.
Two minutes later substitute Stuart Beavon, on for Phillips at half-time, fired a cross-shot a foot wide of the far post from 18 yards.
The Chairboys' more attacking outlook was rewarded in the 56th minute when Akinde beat Sol Davis to a long ball played in behind the full-back, before cutting inside and beating Dean Brill inside his near post with a left-foot strike from 15 yards.
Luton made a double substitution just after the hour as Kevin Gallen and Lewis Emanuel replaced Jarvis and Henderson respectively.
The change helped the Hatters get hold of possession, but the closest they came to forcing an equaliser was Emanuel's speculative angled drive that flew harmlessly wide in the 79th minute.